A critically damped simple harmonic oscillator - Find Friction

[muskaanhamad]

Homework Statement

A critically damped simple harmonic oscillator starts from an amplitude of 5.0 cm and comes to rest at equilibrium 3.5 sec later. The simple harmonic oscillator is made of a .58 kg mass hanging from a spring with spring constant 150 N/m. Assuming the friction force is in the vertical direction, how big is the friction force?

Relevant Equations

Critically Damping factor c = 2√(km)
Friction force = -cv
Velocity v=disp/time

c = Critically Damped factor
c = 2√(km)
c = 2 × √(150 × .58) = 18.65
Friction force = -cv
Velocity v = disp/time = .05/3.5
Friction force = - 18.65 * .05/3.5 = -.27 N

I am not sure if above is correct. Please check and let me know how to do it.

 

[BvU]

Hello @muskaanhamad , !

Velocity v = disp/time = .05/3.5

I can't agree with that: you calculate an average velocity so you find an average force.
Unfortunately, the wording of the problem statement is unclear: 'the force' ?

I did a simulation of your scenario:

and as you can see the force starts at -7.5 N (namely $-x_0*k$) when the acceleration is greatest.
I have no idea what the exercise composer means when he/she asks for 'the force'...